Question

Assume that guesses are made for 4 questions on a medical admissions test such that the probability of success​ (correct) is given by pequals0.30​, where there are nequals4 trials. Find the probability that the number x of correct answers is exactly 2.

Answer 1

0.2646 is the probability that exactly 2 questions are correctly answered.

Explanation:

We are given the following information:

We treat correct as a success.

P(success) = 0.30

Then the number of correct answers follow a binomial distribution, where

`P(X=x) = \binom{n}{x}.p^x.(1-p)^(n-x)`

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 4

We have to evaluate:

`P(x =2)\\= \binom{4}{2}(0.30)^2(1-0.30)^2\\= 0.2646`

0.2646 is the probability that exactly 2 questions are correctly answered.